There are basically four recognized companies in HK: Aeropet, Wish You Were Here, Ferndale Kennels, and Export-a-Pet. I asked for quotes from all of them to import my dog, and there was a difference of HKD2000 between the cheapest and most expensive (also, same service).
I eventually decided to go with an international moving company. They appoint pet shippers to handle the export (from your home country) and import (into HK) aspects. The total cost for export and import is less than the import cost of the most expensive HK company.
Unfortunately, I haven't moved yet. So I can not relate the whole experience. I can only hope everything works out!

(Good for you for taking your pet with you!)